PLEASE HELP BRO!!!!!

Mathematics

1 answer:

guajiro [1.7K]2 years ago

4 0

Answer:

4 and 32

Step-by-step explanation:

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(Zoom in so you can see) I need help on my math homework plz can somebody plz help me out thanks and plz put it correctly thank

murzikaleks [220]

You need to find the area of one of those bigger triangles, and one of those smaller triangles. Then multiply each area by 6 (because there are 6 sides of the big triangles, and the 6 small triangles make up the other side) and add them together. The area of a triangle is 1/2 times base times height equals area.... Equation: 1/2 (b * h) = A

7 0

3 years ago

A) Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given cur

Leno4ka [110]

(a) See the attached sketch. Each shell will have a radius y chosen from the interval [2, 4], a height of x = 2/y, and thickness ∆y. For infinitely many shells, we have ∆y converging to 0, and each super-thin shell contributes an infinitesimal volume of

2π (radius)² (height) = 4πy

Then the volume of the solid is obtained by integrating over [2, 4]:

$\displaystyle 4\pi \int_2^4 y\,\mathrm dy = 2\pi y^2\bigg|_{y=2}^{y=4} = 2\pi (4^2-2^2) = \boxed{24\pi}$

(b) See the other attached sketch. (The text is a bit cluttered, but hopefully you'll understand what is drawn.) Each shell has a radius 9 - x (this is the distance between a given x value in the orange shaded region to the axis of revolution) and a height of 8 - x ³ (and this is the distance between the line y = 8 and the curve y = x ³). Then each shell has a volume of

2π (9 - x)² (8 - x ³) = 2π (648 - 144x + 8x ² - 81x ³ + 18x ⁴ - x ⁵)

so that the overall volume of the solid would be

$\displaystyle 2\pi \int_0^2 (648-144x+8x^2-81x^3+18x^4-x^5)\,\mathrm dx = \boxed{\frac{24296\pi}{15}}$